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Find f(g(x)),g(f(x)),f(f(x)),g(g(x)) `f(x)=x/(x+3) ` `g(x)=2/x.` ``Need answer by tonight.

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libbysimone | (Level 1) Salutatorian

Posted January 15, 2012 at 11:09 AM via web

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Find f(g(x)),g(f(x)),f(f(x)),g(g(x))

`f(x)=x/(x+3) `

`g(x)=2/x.`

``

Need answer by tonight.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted January 15, 2012 at 12:00 PM (Answer #1)

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`f(x)= x/(x+3)`

`g(x)= 2/x`

`f(g(x))= f(2/x)= (2/x)/(2/x + 3) = 2/(2+3x) `

`==gt f(g(x))= 2/(2+3x) `

`g(f(x))``= g(x/(x+3)) = 2/(x/(x+3)) `

`= (2(x+3))/x = (2x+6)/x = 2+ 6/x `

`==gt g(f(x))= 2+ 6/x`

`f(f(x))= f(x/(x+3)) = (x/(x+3))/(x/(x+3) + 3)`

`= x/(x+3(x+3)) `

`x/(x+3x+9)`

`= x/(4x+9) `

`==gt f(f(x))= x/(4x+9)`

`g(g(x))= g(2/x) = 2/(2/x) = x`

`==gt g(g(x))= x`

``

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